Recently, a math professor, with a very impressive set of mathematical papers. made a comment that took me by surprise. I am very open to the feedback. I wanted to open it up here to see what others think.
The professor pointed out that I was duplicating standard reasoning in my question. He suggested that I not think about the Collatz Conjecture at all. He suggested that if I do decide to reject this advice, at least read lots of previous work on the problem so as not to merely redo it (for the record, I've been going through each of the articles referenced in the Wikipedia article, I am reading through Terence Tao's paper on Collatz Conjecture as I have time).
I told the professor that I would be glad to delete the question if he could point me to a paper that covered the same topic (If anyone here points out a paper on the topic of divergent collatz sequences that covers the same ground as my question, I am very glad to delete the question).
I think that implicit in the comment is a compliment. There's an assumption that my mathematical understanding is strong enough that there was no need for my question. The assumption is that if I read more papers on the topic, I might be able to ask a question that did not involve standard reasoning (to be honest, it is my greatest regret that I did not pursue a masters in mathematics -- and that I have so many gaps in my understanding). I agree that spending time on the Collatz Conjecture will most likely not lead to any significant mathematical output. Unfortunately, I suspect that any other topic that I chose to spend my time on would suffer the same fate. I love learning and growing my mathematical ability. I have a very long way to go before my mathematical output merits getting published.
I wondered what others thought about this comment. This is great advice for the professional mathematician and the promising mathematic student. For me, my goal is to learn as much as possible and continuously improve the quality of my questions. While this is my goal, it is true (and I think that this is the professor's point), I may not be accomplishing this goal as much as I should.
I am not clear how to find math papers that fit my questions. I can go to Google. I can read through a Wikipedia article. I can go to Google Scholar. I buy books such as this. I would be glad if anyone has thoughts. How do mathematicians find out if a relevant paper has already been published?
I am a math amateur. I am active on this web site solely because I am trying to learn to think more clearly about mathematics. Being active on this site humbles me and helps me to appreciate the beauty of mathematics.
When I pose a question on this site, I typically spend 2-3 hours writing it, checking the results, and making sure that there are no typos or mistakes in reasoning. Typically, my questions reveal mistakes in my reasoning or assumptions that are not valid. For this reason, I get great satisfaction and value from reading comments and the answers given to my questions.
I greatly enjoy learning and really appreciate the MSE community for supporting me in my pursuit to better understand number theory.
As far as topics, I do not really choose what I am interested in. I wish I could. Certain topics are interesting to me. Others are not. I am a software engineer by profession. Programming comes very easy to me. Mathematics which is more interesting to me does not. I get so many mathematical ideas in my head that if I could somehow do a better job of filtering out the "standard reasoning", then perhaps, I might greatly improve the questions that I ask. They seem great until I type them up as questions.
50% of the questions that I start to ask, I delete before I finish writing them up because I change my mind on whether it was worth asking.